Embodiments according to the invention relate to wireless communication systems, especially wireless multiuser multiple-input multiple-output (MIMO) communications, and particularly to a method and an apparatus for determining a precoding matrix for precoding symbols to be transmitted to a plurality of wireless devices by a node of a wireless communication system.
In the down link of multiuser MIMO communications systems, precoding design and the scheduling of users are the key to achieve high capacity and low inter-user interference. A precoding method with zero forcing (ZF) is mainly used for this purpose and it can cancel out fully the inter-user interference if perfect channel state information is obtained at the transceiver.
As another precoding method to realize the constant modulus property, a precoding method of multiuser MIMO defined in Rel. 8 is available. Although this precoder has the constant modulus property, it can not adequately mitigate low inter-user interference. This is mainly because this method is based on single-user MIMO technologies and the number of precoding matrices is limited by the number of codebooks.
An example for a conventional method is a ZF precoding based on channel vector quantization (CVQ). At the eNB (evolved node B), the precoded signal xεM is transmitted over M antennas and received by N antennas at the terminal. With the kth users' channel matrix HkεN×M and the complex white Gaussian noise term nkεN (each entry has variance one), the received signal can be written asyk=Hkx+nk  (1)
In case of non-codebook based precoding at the eNB, each terminal (wireless device) provides a Channel Direction Indicator (CDI) together with a Channel Quality Indicator (CQI) via the feedback channel. Here, the CDI is an entry in the codebook (usually represented by a codebook index)C={u1,u2, . . . , u2B}  (2)which is obtained via Channel Vector Quantization (CVQ) of the composite channel vector heff,kT=wkTHkε1×M, i.e., the combination of the channel Hk and the receive filter wk at user k. Since the finally used Minimum Mean Square Error (MMSE) receive filter of user k depends on the finally chosen precoder which is not known at the time of CVQ because the channels of other users are unknown due to the non-cooperative nature of the downlink channel, the receiver needs to be estimated as described in “3GPP, R1-070346, Philips, “Comparison of MU-MIMO feedback schemes with multiple UE receive antennas””. In other words, the quantizer QC computes not only the quantized composite channel vector ĥeff,k but also a receiver estimate ŵk both depending on the type of CVQ:CDI: (ĥeff,k,ŵk)=QC(Hk)  (3)
Due to the fact that the channels of other users and the finally chosen precoder is not known when the feedback information is computed at a terminal, the SINR as the CQI is to be approximated by taking into account a rough estimate of the multiuser interference caused by the imperfect channel state information at the eNB due to quantization (see “3GPP, R1-070346, Philips, “Comparison of MU-MIMO feedback schemes with multiple UE receive antennas”” for details):
                                          CQI            ⁢                          :                        ⁢                                                  ⁢                                          γ                k                            ⁡                              (                                                                            h                      ^                                                              eff                      ,                      k                                                        ,                                                            w                      ^                                        k                                    ,                                      H                    k                                                  )                                              =                                                                      P                  Tx                                M                            ⁢                                                                                                            H                      k                      T                                        ⁢                                                                  w                        k                                            ^                                                                                        2                2                            ⁢                              cos                2                            ⁢                              θ                k                                                    1              +                                                                    P                    Tx                                    M                                ⁢                                                                                                                        H                        k                        T                                            ⁢                                                                        w                          k                                                ^                                                                                                  2                  2                                ⁢                                  sin                  2                                ⁢                                  θ                  k                                                                    ,                              cos            ⁢                                                  ⁢                          θ              k                                =                                                                                                        h                    ^                                                        eff                    ,                    k                                                  ⁢                                  H                  k                  T                                ⁢                                                      w                    k                                    ^                                                                                                                                                        H                    k                    T                                    ⁢                                                            w                      k                                        ^                                                                              2                                                          (        4        )            
Whereas the CQI values are used at the eNB to schedule the users in a greedy way as described in 23GPP, R1-070346, Philips, “Comparison of MU-MIMO feedback schemes with multiple UE receive antennas”” and “3GPP, R1-062483, Philips, “Comparison between MU-MIMO codebook-based channel reporting techniques for LTE downlink”” and to choose the proper MCS (Modulation and Coding Scheme), the CDIs are used to generate the composite channel matrix ĤeffεD×M with rows according to the quantized composite channel vectors of the D scheduled users (wireless devices). Note that at maximum one data stream (symbol) per user is assumed, thus, D is also the number of simultaneously transmitted data streams. With s being the D-dimensional vector of scheduled symbols and assuming a Zero-Forcing (ZF) transmission scheme, the ZF precoder is computed asPZF=Ĥeff(ĤeffĤeffH)−1  (5)
The precoded signal computes asx=PZFDs  (6)where D is a diagonal matrix with elements chosen for equal power loading.
Next, an implementation (Euclidean distance based CVQ) of the quantizer Qc is described. Other implementations of quantizer like SINR based CVQ are also applicable.
Remember that one problem of CVQ is the fact that the finally chosen MMSE receive filter (Minimum Mean Square Error receive filter) is not known when the terminal computes the feedback information due to its dependency on the finally chosen precoder and this precoder cannot be computed at the terminals because of the lack of knowledge about the channel state information at other terminals (non-cooperative nature of the downlink channel). To overcome this obstacle, one assumes firstly an arbitrary receive filter. Since the resulting composite channel vector is then an arbitrary linear combination of the rows of Hk, it lies in the row space of Hk. This fact can be exploited for CVQ in the sense that the codebook entry is chosen such that the distance to the row space of Hk is minimized. However, for computing the CQI, one needs not only the quantized composite channel vector but also an estimate of the receive filter. In the case of Euclidean distance based CVQ, the receive filter is also chosen such that the resulting composite channel vector in the row space of Hk has the minimum Euclidean distance from the quantized channel vector. Note that the optimization criterion of the resulting receive filter is no longer the mean-squared error like in the finally applied MMSE receiver but the Euclidean distance. This leads to a mismatch between true SINR and the one fed back as the CQI and used for scheduling. Finally, the procedure of the Euclidean distance based CVQ method can be summarized as follows:
                                                        Q              C              Euclid                        ⁢                          :                        ⁢                                                  ⁢                          H              k                                ↦                      (                                                            h                  ^                                                  eff                  ,                  k                                            ,                                                w                  k                                ^                                      )                          ,                                                                                                                        h                      ^                                                              eff                      ,                      k                                                        =                                                            argmax                                              u                        ∈                        C                                                              ⁢                                                                                                                                                Q                            k                            H                                                    ⁢                          u                                                                                            2                                                                      ,                                                      H                    k                                    =                                                            Q                      k                                        ⁢                                                                  R                        k                                            ⁡                                              (                                                  QR                          ⁢                                                                                                          ⁢                          decomposition                                                )                                                                                                                                                                                                          w                    ^                                    k                                =                                                                                                    (                                                                                                            H                              k                              H                                                        ⁡                                                          (                                                                                                H                                  k                                                                ⁢                                                                  H                                  k                                  H                                                                                            )                                                                                                            -                            1                                                                          )                                            T                                        ⁢                                          Q                      k                                        ⁢                                          Q                      k                      H                                        ⁢                                                                  h                        ^                                                                    eff                        ,                        k                                                                                                                                                                                                                            (                                                                                                                            H                                  k                                  H                                                                ⁡                                                                  (                                                                                                            H                                      k                                                                        ⁢                                                                          H                                      k                                      H                                                                                                        )                                                                                                                            -                                1                                                                                      )                                                    T                                                ⁢                                                  Q                          k                                                ⁢                                                  Q                          k                          H                                                ⁢                                                                              h                            ^                                                                                eff                            ,                            k                                                                                                                                      2                                                                                                          (        7        )            
In the following, details of zero forcing (ZF) beamforming method are explained using figures. FIG. 8a shows a schematic illustration of a multiuser MIMO (MU-MIMO) system with a base station and two wireless devices (user equipment UE). It illustrates a target configuration for downlink transmission in a multiuser MIMO system. For this, a precoding design and its optimization method for energy savings is desired. In this example, the base station comprises four antennas and each wireless device comprises two antennas. Further, FIG. 8b shows a schematic illustration of the precoding of data. The precoding matrix is used for precoding data for each antenna of the base station and the power amplifiers (PA) of each antenna amplify a corresponding data signal for transmission.
For this, first the base station collects channel state information (ĥ1,eff to ĥL,eff) from the wireless devices, as it is indicated in FIG. 9, where L is the number of the wireless devices. For precoding with zero forcing (ZF) beamforming method, channel state information ĥ1,eff,ĥL,eff is received from the wireless devices at the node. Based on the feedback from the wireless devices (the UE), a composite channel (composite channel matrix) Ĥeff may be calculated. The composite channel may indicate the combination of the measured channel Hk at user k and the received filter wk at user k. Then, the zero forcing ZF precoder PZF may be calculated.
                    H        ^            eff        =          ⌊                                    h            ^                                1            ,            eff                          ,        …        ⁢                                  ,                              h            ^                                L            ,            eff                              ⌋                  P      ZF        =                                                      H              ^                        eff            H                    ⁡                      (                                                            H                  ^                                eff                            ⁢                                                H                  ^                                eff                H                                      )                                    -          1                    ZF      
The mathematical background for precoding data according to the zero forcing concept is illustrated in FIG. 10. It shows an example for two transmit antennas (TX) and two wireless devices (UE, user equipment). As it can be seen, the transmit power Pa1, Pa2 between the antennas is unequal. The precoded data is then transmitted to the wireless devices. At the wireless devices the receive signals are filtered by a receive filter W to obtain the transmitted data.
However, the ZF precoder (a device which has a precoding function is referred as a precoder) obtained by Equation (5) doesn't possess a constant modulus property. Here, the constant modulus property means pure phase corrections—that is, with no amplitude changes. Therefore, the ZF precoder unequally loads the transmit power for each antenna. Each PA (power amplifier) needs to output higher transmit power than that of a precoder fulfilling the property. As a result, the power consumption of each PA will become higher.